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Mathematics > Combinatorics

arXiv:2207.08542 (math)
[Submitted on 18 Jul 2022 (v1), last revised 7 Nov 2022 (this version, v2)]

Title:Generations of random hypergraphs and random simplicial complexes by the map algebra

Authors:S. Ren
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Abstract:We consider the random hypergraph on a finite vertex set by choosing each set of vertices as an hyperedge independently at random. We express the probability distributions of the (lower-)associated simplicial complex and the (lower-)associated independence hypergraph of the random hypergraph in terms of the probability distributions of certain random simplicial complex and certain random independence hypergraph of Erdös-Rényi type. We construct a graded structure of the map algebra explicitly and give algorithms to generate random hypergraphs and random simplicial complexes.
Comments: 20 pages
Subjects: Combinatorics (math.CO)
MSC classes: Primary 05C80, 05E45, Secondary 55U10, 68P05
Cite as: arXiv:2207.08542 [math.CO]
  (or arXiv:2207.08542v2 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.2207.08542

Submission history

From: Shiquan Ren [view email]
[v1] Mon, 18 Jul 2022 12:08:13 UTC (26 KB)
[v2] Mon, 7 Nov 2022 23:51:28 UTC (20 KB)
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